a little bit more fancy way would be to write a small little program in processing which receive all the data from the serial port and print it to a text file, if you want i can pass the code to you, but on the other hand it is really easy, you know the processing GUI is the same as for Ardunio,

If you use hyperterminal then it is easy to save any incoming serial data. Just connect to your Arduino, and then go to the 'Transfer->Capture Text' menu option. Select a file to save your data and away you go! All incoming serial data will then be automatically saved for you.